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Homework Help: Improper Integral Convergence

  1. Feb 19, 2009 #1
    1. The problem statement, all variables and given/known data
    I'm trying to show that this improper integral converges
    [tex]\int_{0}^{1} \sin \left ( x + \frac{1}{x} \right )dx[/tex]

    2. Relevant equations

    3. The attempt at a solution
    I thought a comparison test would be nice but I can't think of the right one if that is the way to go. I don't think a substitution of u = x + 1/x works too well as well.

  2. jcsd
  3. Feb 19, 2009 #2


    Staff: Mentor

    -1 <= sin(x + 1/x) <= 1
  4. Feb 19, 2009 #3
    I see. Thanks.
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